Juan C. Moreno

Department of Mathematics

University of Notre Dame

Office: Hurley 260

Email: jmoreno9@nd.edu

Pronouns: he/him

About Me

I am a Postdoctoral Research Associate at the University of Notre Dame Department of Mathematics, working with Mark Behrens.

I completed my Ph.D. in Spring 2025 at the University of Colorado Boulder, advised by Agnès Beaudry.

Before that, I was an undergraduate at the University of Texas at Austin, where I received Bachelors of Science in math and physics.

My research interests lie generally in the areas of stable homotopy theory, and interactions between algebraic topology and physics.

You can find my CV here (last updated Nov. 2024).

Research

Ongoing

The Real v_n-Bockstein spectral sequence.

The pictures at the top and bottom of this page illustrate a Bockstein spectral sequence computing the homotopy groups of tmf_0(3) from the RO(C_2)-graded homotopy groups of Atiyah Real K-theory. I'm currently thinking about generalizations of this computation to truncated norms of Real bordism.

Telescopes and the F_p-synthetic ANSS

With Mark Behrens, we study localizations of the F_p-synthetic ANSS of certain synthetic spectra. Of particular interest to us are the synthetic analogs of the Mahowald--Ravenel--Schick Thom spectra y(n).

Preprints

On homological Real trace methods. (2026) ArXiv version. Submitted.

With Myungsin Cho, Teena Gerhardt, Liam Keenan, and J.D. Quigley.

Publications

Duals of higher real K-theories at p=2. ArXiv version.

Advances in Mathematics (2026). Published version.

Homotopical Foundations of Parametrized Quantum Spin Systems. ArXiv version.

With A. Beaudry, M. Hermele, M. Pflaum, M. Qi, and D. Spiegel.

Reviews in Mathematical Physics (2024). Published version.

Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems. ArXiv version.

With X. Wen, D. Spiegel, A. Beaudry, M. Qi, M. Hermele, A. Vishwanath, and M. Pflaum.

Phys. Rev. B. Volume 108, Issue 12. American Physical Society (2022). Published version.

Continuous Dependence on the Initial Data in the Kadison Transitivity Theorem and GNS Construction. ArXiv version.

With D. Spiegel, M. Qi, M. Hermele, A. Beaudry, and M. Pflaum.

Reviews in Mathematical Physics (2022). Published version.

Notes

Real topological cyclic homology of F_2 via the slice filtration. Link (Last updated: 09/02/26)

Teaching

University of Notre Dame

Fall 2026 Instructor MATH 10350 Calculus A
Spring 2026 Instructor MATH 20580 Intro to linear algebra & differential equations.
Fall 2025 Instructor MATH 10350 Calculus A

University of Colorado Boulder

Spring 2025 Instructor MATH 2300 Calculus 2
Spring 2024 TA MATH 2300 Calculus 2
Spring 2023 TA MATH 2300/2400 Calculus 2/3
Fall 2022 Instructor MATH 2400 Calculus 3
Fall 2021 Instructor MATH 2300 Calculus 2
Spring 2021 TA MATH 2400 Calculus 3
Spring 2020 TA MATH 2300 Calculus 2
Fall 2019 TA MATH 1300 Calculus 1

University of Texas at Austin

Spring 2018 LA M408S Integral Calculus for Science
Fall 2017 LA M408L Integral Calculus